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Multivariate Stochastic Volatility with Cross Leverage


  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)


We describe and estimate for the first time a natural multivariate extension of the univariate stochastic volatility model with leverage. The model, which we call the multivariate stochastic volatility with cross leverage, is fit by a tuned Bayesian MCMC method. Of particular general interest is our approach for sampling the state variables from the posterior distribution conditioned on the parameters. The state variables are sampled in blocks by the Metropolis-Hastings algorithm in which the proposal density is derived from an approximating linear Gaussian state space model. The conditional modes of the latent volatility variables are computed using a method of scoring where the covariance matrix of the proposal density is guaranteed to be positive definite. The auxiliary particle filter to compute the likelihood function is also shown and the model and the techniques are illustrated with daily stock returns data from the Tokyo Stock Exchange.

Suggested Citation

  • Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Multivariate Stochastic Volatility with Cross Leverage," CARF F-Series CARF-F-191, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf191

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    References listed on IDEAS

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    12. Chia-Lin Chang & Michael McAleer & Christine Lim, 2009. "Modelling Short and Long Haul Volatility in Japanese Tourist Arrivals to New Zealand and Taiwan," CIRJE F-Series CIRJE-F-647, CIRJE, Faculty of Economics, University of Tokyo.
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    14. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    15. Chia-Lin Chang & Michael McAleer & Dan Slottje, 2009. "Modelling International Tourist Arrivals and Volatility: An Application to Taiwan," "Marco Fanno" Working Papers 0097, Dipartimento di Scienze Economiche "Marco Fanno".
    16. Chang, Chia-Lin & Sriboonchitta, Songsak & Wiboonpongse, Aree, 2009. "Modelling and forecasting tourism from East Asia to Thailand under temporal and spatial aggregation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1730-1744.
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    Cited by:

    1. Kurose, Yuta & Omori, Yasuhiro, 2016. "Dynamic equicorrelation stochastic volatility," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 795-813.
    2. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    3. Caporin, Massimiliano & McAleer, Michael, 2014. "Robust ranking of multivariate GARCH models by problem dimension," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 172-185.
    4. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    5. Diks, Cees & Panchenko, Valentyn & Sokolinskiy, Oleg & van Dijk, Dick, 2014. "Comparing the accuracy of multivariate density forecasts in selected regions of the copula support," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 79-94.
    6. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 642-654.
    7. Caldeira, João F & Moura, Guilherme Valle & Santos, André Alves Portela, 2013. "Seleção de carteiras utilizando o modelo Fama-French-Carhart," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 67(1), April.
    8. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    9. Asai, Manabu & Caporin, Massimiliano & McAleer, Michael, 2015. "Forecasting Value-at-Risk using block structure multivariate stochastic volatility models," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 40-50.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    11. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," "Marco Fanno" Working Papers 0124, Dipartimento di Scienze Economiche "Marco Fanno".
    12. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    13. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 606-617.
    14. Caporin, Massimiliano, 2013. "Equity and CDS sector indices: Dynamic models and risk hedging," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 261-275.
    15. repec:fgv:epgrbe:v:67:n:1:a:3 is not listed on IDEAS
    16. Geert Mesters & Bernd Schwaab & Siem Jan Koopman, 2014. "A Dynamic Yield Curve Model with Stochastic Volatility and Non-Gaussian Interactions: An Empirical Study of Non-standard Monetary Policy in the Euro Area," Tinbergen Institute Discussion Papers 14-071/III, Tinbergen Institute.
    17. Trojan, Sebastian, 2014. "Multivariate Stochastic Volatility with Dynamic Cross Leverage," Economics Working Paper Series 1424, University of St. Gallen, School of Economics and Political Science.
    18. Sujay K Mukhoti, "undated". "Dynamic Feedback Effect And Skewness In Non-Stationary Stochastic Volatility Model With Leverage," Working papers 145, Indian Institute of Management Kozhikode.

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